Variational model of thermal explosion in an ellipsoid of revolution

Abstract

According to the formulation of the nonlinear problem of stationary heat conduction in a homogeneous ellipsoid, when the intensity of volume energy release increases with temperature, a variational form of a mathematical model of a thermal explosion has been developed. This form contains a functional defined on a set of continuous and piecewise differentiable functions. These functions approximate the temperature distribution in the ellipsoid volume and accept a given temperature on its surface. The study of stationary points of the functional makes it possible to estimate a combination of defining parameters in which the temperature state in the ellipsoid precedes the thermal explosion. A quantitative analysis of the variational form of the model has been carried out with the exponential growth of the energy release intensity with temperature increase. The study introduces a relation for estimating an integral error arising when a specific approximating function is used. The comparison of such estimates for various approximating functions makes it possible to choose the function closest to the temperature distribution preceding the thermal explosion in the ellipsoid.